PART 1:[br][br]1.In each of the polygons, pick one vertex and draw all of the diagonals from that vertex. Notice how this divides [br]each polygon into triangular regions[br][br]2.After you have drawn in all of the diagonals, complete the table on your worksheet.[br][br]3.Make a conjecture about the sum of the interior angles of any convex polygon.[br][br]4.Draw your own polygons of any size and test your conjecture!

PART 2:[br][br]1. Using the "Ray through 2 points" told, start at one vertex and extend a ray through the next vertex moving counterclockwise. Do this until the sides of the polygon are all extended by rays.[br][br]2. Using the "New Point" tool, plot a point on each of the rays that you have created on the figure- the points must be plotted on the ray outside of the polygon (do not place them on the polygon).[br][br]3. Using the angle tool, measure the exterior angles of the polygon, moving in a counterclockwise rotation. (To do this, you must select the 3 points that you want to make up the angle. Start by selecting one of the points that you plotted, then the two vertexes counterclockwise to that point.)[br][br]4. Record the number of sides of the polygon along with the measures of its exterior angles.[br][br]5. Find the sum of the interior angles of each polygon.[br][br]6. Make a conjecture about the sum of the exterior angles of a convex polygon.[br][br]7. How could we prove this?

[b]Click the "▶" button. Observe the angles turned by the car at the corners.[br]Drag the green points. Check the "Show Measurement" box to see the measurements of the angles.[br][/b]中文版：[url=https://ggbm.at/551]https://ggbm.at/551[/url]

[b]1. What is a + b + c + d + e, the total angles turned by the car?[br]2. a, b, c, d, e are called the exterior angles of the convex pentagon.[br]　　In general, what is the sum of all exterior angles of a convex polygon?[br]3. How would you modify the result if the pentagon is NOT convex?[br][/b][br]Anthony Or. GeoGebra Institute of Hong Kong.